A markov model based analysis of stochastic biochemical systems.

The molecular networks regulating basic physiological processes in a cell are generally converted into rate equations assuming the number of biochemical molecules as deterministic variables. At steady state these rate equations gives a set of differential equations that are solved using numerical methods. However, the stochastic cellular environment motivates us to propose a mathematical framework for analyzing such biochemical molecular networks. The stochastic simulators that solve a system of differential equations includes this stochasticity in the model, but suffer from simulation stiffness and require huge computational overheads. This paper describes a new markov chain based model to simulate such complex biological systems with reduced computation and memory overheads. The central idea is to transform the continuous domain chemical master equation (CME) based method into a discrete domain of molecular states with corresponding state transition probabilities and times. Our methodology allows the basic optimization schemes devised for the CME and can also be extended to reduce the computational and memory overheads appreciably at the cost of accuracy. The simulation results for the standard Enzyme-Kinetics and Transcriptional Regulatory systems show promising correspondence with the CME based methods and point to the efficacy of our scheme.